(* ::Package:: *)

 


(* ::Section:: *)
(* GAE *)


(* ::Text:: *)
(*`GAE[\[Mu]]` can be used as input for a `D-4`-dimensional $\gamma^{\mu }$and is transformed into `DiracGamma[LorentzIndex[$\mu$,D-4],D-4]` by `FeynCalcInternal` (`FCI`). *)


(* ::Text:: *)
(*`GAE[$\mu ,\nu , \text{...}$]` is a short form for `GAE[$\mu$].GAE[$\nu$]. ...`.*)


(* ::Subsection:: *)
(* See also *)


(* ::Text:: *)
(*DiracGamma, GA, GS, GAD.*)


(* ::Subsection:: *)
(* Examples *)


GAE[\[Mu]]


GAE[\[Mu],\[Nu]]-GAE[\[Nu],\[Mu]]


StandardForm[FCI[GAE[\[Mu]]]]


GAE[\[Mu],\[Nu],\[Rho],\[Sigma]]


StandardForm[GAE[\[Mu],\[Nu],\[Rho],\[Sigma]]]


GAE[\[Alpha]] FVD[p,\[Alpha]]//Contract


GAE[\[Alpha]] FV[p,\[Alpha]]//Contract


(* ::Text:: *)
(*In order to use Dirac algebra with $D-4$-dimensional objects you need to activate the t'Hooft-Veltman-Breitenlohner-Maison scheme first*)


FCSetDiracGammaScheme["NDR"]
DiracSimplify[GAE[\[Mu]] . GAD[\[Mu]]]


FCSetDiracGammaScheme["BMHV"]
DiracSimplify[GAE[\[Mu]] . GAD[\[Mu]]]


FCSetDiracGammaScheme["NDR"]
